Examples with solutions for Addition and Subtraction of Decimal Fractions: Solving the problem

Exercise #1

Solve the following exercise and circle the appropriate answer:

13.29-12.13

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

We'll subtract the hundredths after the decimal point:

93=6 9-3=6

We'll subtract the tenths after the decimal point:

21=1 2-1=1

Finally, we'll subtract the whole numbers before the decimal point accordingly:

32=1 3-2=1

11=0 1-1=0

And we'll get:

13.2912.1301.16 13.29\\-12.13\\01.16

Answer

1.16

Exercise #2

Solve the following exercise and circle the appropriate answer:

21.38+13.41

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

We'll add up the hundredths after the decimal point:

8+1=9 8+1=9

We'll add up the tenths after the decimal point:

3+4=7 3+4=7

Finally, we'll add up the whole numbers before the decimal point accordingly:

1+3=4 1+3=4

2+1=3 2+1=3

And we get:

21.38+13.4134.79 21.38\\+13.41\\34.79

Answer

34.79

Exercise #3

Solve the following exercise and circle the appropriate answer:

3.512+4.313

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

We'll add up the thousandths after the decimal point:

2+3=5 2+3=5

We'll add up the hundredths after the decimal point:

1+1=2 1+1=2

We'll add up the tenths after the decimal point:

5+3=8 5+3=8

Finally, we'll subtract the whole numbers before the decimal point:

3+4=7 3+4=7

And we get:

3.512+4.3137.825 3.512\\+4.313\\7.825

Answer

7.825

Exercise #4

Solve the following exercise:

22.1-12.0

Video Solution

Step-by-Step Solution

Let's solve the exercise in order.

First, we'll subtract the tenths after the decimal point:

10=1 1-0=1

Then, we'll subtract the whole numbers before the decimal point accordingly:

22=0 2-2=0

21=1 2-1=1

We get:

22.112.010.1 22.1\\-12.0\\10.1

Answer

10.1

Exercise #5

Solve the following exercise and circle the appropriate answer:

16.29-13.35

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

Let's subtract the hundreds after the decimal point

95=4 9-5=4

Let's subtract the tenths after the decimal point:

23= 2-3=

Since we cannot subtract, we'll borrow ten from the tens digit of the whole number and get:

123=9 12-3=9

Finally, let's subtract the whole numbers before the decimal point accordingly.

Since we borrowed ten from the tens digit of the whole number we get:

613=2 6-1-3=2

11=0 1-1=0

And we get:

16.2913.3502.94 16.29\\-13.35\\02.94

We can ignore the 0 before the 2, so we got the number: 2.94

Answer

2.94

Exercise #6

Solve the following exercise and circle the appropriate answer:

16.33-15.59

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

Let's subtract the hundreds after the decimal point

39= 3-9=

Since we cannot subtract, we'll borrow ten from the tenths after the decimal point and get:

139=4 13-9=4

Let's subtract the tenths after the decimal point, remembering that we borrowed ten, therefore:

315=25 3-1-5=2-5

Since we cannot subtract, we'll borrow ten from the tens digit of the whole number and get:

125=7 12-5=7

Finally, let's subtract the whole numbers before the decimal point accordingly.

Since we borrowed ten from the tens digit of the whole number we get:

615=0 6-1-5=0

11=0 1-1=0

And we get:

16.3315.5900.74 16.33\\-15.59\\00.74

We can ignore the 0 before the 0 and therefore we got the number: 0.74

Answer

0.74

Exercise #7

Solve the following exercise and circle the appropriate answer:

19.28-15.39

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

Let's subtract the hundreds after the decimal point:

89= 8-9=

Since we cannot subtract, we'll borrow ten from the tenths digit after the decimal point and get:

189=9 18-9=9

Let's subtract the tenths after the decimal point, remembering that we borrowed ten, therefore:

213=13 2-1-3=1-3

Since we cannot subtract, we'll borrow ten from the tens digit of the whole number and get:

113=8 11-3=8

Finally, let's subtract the whole numbers before the decimal point accordingly.

Let's remember that we borrowed ten from the tens digit, therefore:

915=3 9-1-5=3

11=0 1-1=0

And we get:

19.2815.3903.89 19.28\\-15.39\\03.89

We can ignore the zero before the 3 and we got the number: 3.89

Answer

3.89

Exercise #8

Solve the following exercise and circle the appropriate answer:

19.28-17.99

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

Let's subtract the hundreds after the decimal point:

89= 8-9=

Since we cannot subtract, we'll borrow ten from the tenths after the decimal point and get:

189=9 18-9=9

Let's subtract the tenths after the decimal point, remembering that we borrowed ten, therefore:

219=19 2-1-9=1-9

Since we cannot subtract, we'll borrow ten from the tens digit of the whole number and get:

119=2 11-9=2

Finally, let's subtract the whole numbers before the decimal point accordingly.

Since we borrowed ten from the tens digit of the whole number we get:

917=1 9-1-7=1

11=0 1-1=0

And we get:

19.2817.9901.29 19.28\\-17.99\\01.29

We can ignore the 0 before the 1, so we got the number: 1.29

Answer

1.29

Exercise #9

Solve the following exercise and circle the appropriate answer:

28.18-19.29

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

Let's subtract the hundreds after the decimal point:

89= 8-9=

Since we cannot subtract, we'll borrow ten from the tenths after the decimal point and get:

189=9 18-9=9

Let's subtract the tenths after the decimal point, remembering that we borrowed ten, therefore:

112=02 1-1-2=0-2

Since we cannot subtract, we'll borrow ten from the tens digit of the whole number and get:

102=8 10-2=8

Finally, let's subtract the whole numbers before the decimal point accordingly.

Since we borrowed ten from the tens digit of the whole number, we get:

819=79 8-1-9=7-9

Since we cannot subtract, we'll borrow ten from the ones digit of the whole number and get:

179=8 17-9=8

Remember that we borrowed ten from the ones digit, therefore we get:

211=0 2-1-1=0

And we get:

28.1819.2908.89 28.18\\-19.29\\08.89

We can ignore the 0 before the 8, so we got the number: 8.89

Answer

8.89

Exercise #10

Solve the following exercise and circle the appropriate answer:

33.10-11.10

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

We'll subtract the hundreds after the decimal point:

00=0 0-0=0

We'll subtract the tenths after the decimal point:

11=0 1-1=0

Finally, we'll subtract the whole numbers before the decimal point accordingly:

31=2 3-1=2

31=2 3-1=2

And we get:

33.1011.1022.00 33.10\\-11.10\\22.00

Since there are only zeros after the decimal point, we can ignore them and we actually got the number: 22

Answer

22

Exercise #11

Solve the following exercise:

12.0+29.31

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will first add the digit 0 to the number 12.0 as follows:

12.00+29.31 12.00\\+29.31\\

Now let's solve the exercise in order:

Let's add the hundreds after the decimal point:

0+1=1 0+1=1

Let's add the tenths after the decimal point:

0+3=3 0+3=3

Finally, let's add the whole numbers before the decimal point:

2+9=11 2+9=11

We'll add ten to the ones digit before the decimal point and get:

1+1+2=4 1+1+2=4

And we get:

12.00+29.3141.31 12.00\\+29.31\\41.31

Answer

41.31

Exercise #12

Solve the following exercise:

32.1+37.032

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we'll first add two zeros to the number 32.1 as follows:

32.100+37.032 32.100\\+37.032\\

Now let's solve the exercise in order:

Let's multiply the thousandths after the decimal point:

0+2=2 0+2=2

Let's multiply the hundredths after the decimal point:

0+3=3 0+3=3

Let's multiply the tenths after the decimal point:

1+0=1 1+0=1

Finally, let's multiply the whole numbers before the decimal point accordingly:

2+7=9 2+7=9

3+3=6 3+3=6

And we get:

32.100+37.03269.132 32.100\\+37.032\\69.132

Answer

69.132

Exercise #13

Solve the following exercise:

123.421+615.3

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will first add two zeros to the number 615.3 as follows:

123.421+615.300 123.421\\+615.300\\

Now let's solve the exercise in order:

Let's connect the thousandths after the decimal point:

1+0=1 1+0=1

Let's connect the hundredths after the decimal point:

2+0=2 2+0=2

Let's connect the tenths after the decimal point:

4+3=7 4+3=7

Finally, let's connect the whole numbers before the decimal point accordingly:

3+5=8 3+5=8

2+1=3 2+1=3

1+6=7 1+6=7

And we get:

123.421+615.300738.721 123.421\\+615.300\\738.721

Answer

738.721

Exercise #14

Solve the following exercise:

321.301+210.1

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will first add two zeros to the number 210.1 as follows:

321.301+210.100 321.301\\+210.100\\

Now let's solve the exercise in order:

Let's connect the thousandths after the decimal point:

1+0=1 1+0=1

Let's connect the hundredths after the decimal point:

0+0=0 0+0=0

Let's connect the tenths after the decimal point:

3+1=4 3+1=4

Finally, let's connect the whole numbers before the decimal point accordingly:

1+0=1 1+0=1

2+1=3 2+1=3

3+2=5 3+2=5

And we get:

321.301+210.100531.401 321.301\\+210.100\\531.401

Answer

531.401

Exercise #15

Solve the following exercise:

131.2+312.522

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will first add two zeros to the number 131.2 as follows:

131.200+312.522 131.200\\+312.522\\

Now let's solve the exercise in order:

Let's connect the thousandths after the decimal point:

0+2=2 0+2=2

Let's connect the hundredths after the decimal point:

0+2=2 0+2=2

Let's connect the tenths after the decimal point:

2+5=7 2+5=7

Finally, let's connect the whole numbers before the decimal point accordingly:

1+2=3 1+2=3

3+1=4 3+1=4

1+3=4 1+3=4

And we get:

131.200+312.522443.722 131.200\\+312.522\\443.722

Answer

443.722

Exercise #16

Circle the correct answer to the following exercise:

18-16.31

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will first add two zeros to the number 18 as follows:

18.0016.31 18.00\\-16.31\\

Now let's solve the exercise in order:

Let's subtract the hundreds after the decimal point:

01= 0-1=

Since we cannot solve the exercise, we will borrow ten from the tens digit of the whole number before the decimal point (since the tenths digit after the decimal point is also 0)

Now the tens digit of the whole number before the decimal point will become 7 and the tenths digit after the decimal point will change from 0 to 10

We will borrow ten from the tenths digit after the decimal point and it will change from 10 to 9 and the hundreds digit will change from 0 to 10

Now we can solve the exercise.

Let's subtract the hundreds after the decimal point:

101=9 10-1=9

Let's subtract the tenths after the decimal point:

93=6 9-3=6

Finally, let's subtract the whole numbers before the decimal point accordingly:

816=1 8-1-6=1

11=0 1-1=0

And we get:

18.0016.3101.69 18.00\\-16.31\\01.69

We can ignore the zero before the 1 and therefore we get the number: 1.69

Answer

1.69

Exercise #17

Circle the correct answer to the following exercise:

100-99.318

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will add zeros in the appropriate places.

Three zeros for the number 100 and one zero before the number 99 as follows:

100.000099.318 100.000\\-099.318\\

Now let's solve the exercise in order:

Let's subtract the thousands after the decimal point:

08= 0-8=

Since we cannot subtract, we'll borrow ten from the ones digit of the whole number before the decimal point, since the other numbers are also zeros.

The ones digit of the whole number before the decimal point will become 0, and the tens digit of the whole number before the decimal point will become 10

We'll borrow ten from the tens digit of the whole number before the decimal point and it will change from 10 to 9, and now the hundreds digit of the whole number before the decimal point will become 10

We'll borrow ten from the hundreds digit of the whole number before the decimal point and it will change from 10 to 9, and now the tenths digit after the decimal point will become 10

We'll borrow ten from the tenths digit after the decimal point and it will change from 10 to 9, and now the hundredths digit after the decimal point will become 10

We'll borrow ten from the hundredths digit after the decimal point and it will change from 10 to 9, and now the thousandths digit after the decimal point will become 10

Now that we know how to solve the exercise, let's subtract the thousands after the decimal point:

108=2 10-8=2

Let's subtract the hundreds after the decimal point:

91=8 9-1=8

Let's subtract the tenths after the decimal point:

93=6 9-3=6

Finally, let's subtract the whole numbers before the decimal point accordingly:

99=0 9-9=0

99=0 9-9=0

00=0 0-0=0

And we get:

100.000099.318000.682 100.000\\-099.318\\000.682

We can ignore the first two zeros and therefore get the number: 0.682

Answer

0.682

Exercise #18

Circle the correct answer to the following exercise:

310-110.352

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we'll first add three zeros to the number 310 as follows:

310.000110.352 310.000\\-110.352\\

Now let's solve the exercise in order:

Let's subtract the thousands after the decimal point:

02= 0-2=

Since we cannot subtract, we'll borrow ten from the tens digit of the whole number before the decimal point, since the other numbers are also zeros.

The tens digit of the whole number before the decimal point will become 0, and the hundreds digit of the whole number before the decimal point will become 10

We'll borrow ten from the hundreds digit before the decimal point and it will change from 10 to 9, and now the tenths digit after the decimal point will become 10

We'll borrow ten from the tenths digit after the decimal point and it will change from 10 to 9, and now the hundredths digit after the decimal point will become 10

We'll borrow ten from the hundredths digit after the decimal point and it will change from 10 to 9, and now the thousandths digit after the decimal point will become 10

Now that we know how to solve the exercise, let's subtract the thousands after the decimal point:

102=8 10-2=8

Let's subtract the hundreds after the decimal point:

95=4 9-5=4

Let's subtract the tenths after the decimal point:

93=6 9-3=6

Finally, let's subtract the whole numbers before the decimal point accordingly:

90=9 9-0=9

01= 0-1=

Since we cannot subtract, we'll borrow ten from the ones digit of the whole number and we get:

101=9 10-1=9

Remember that we borrowed ten from the ones digit, so we get:

311=1 3-1-1=1

And we get:

310.000110.352199.648 310.000\\-110.352\\199.648

Answer

199.648

Exercise #19

Circle the correct answer to the following exercise:

76-10.3213

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will first add four zeros to the number 76 as follows:

76.000010.3213 76.0000\\-10.3213\\

Now let's solve the exercise in order:

Let's subtract the tens of thousands after the decimal point:

03= 0-3=

Since we cannot subtract, we'll borrow ten from the tens digit of the whole number before the decimal point, as all other numbers are also zeros.

The tens digit of the whole number before the decimal point will become 5, and the tenths digit after the decimal point will become 10

We'll borrow ten from the tenths digit after the decimal point and it will change from 10 to 9, and now the hundredths digit after the decimal point will become 10

We'll borrow ten from the hundredths digit after the decimal point and it will change from 10 to 9, and now the thousandths digit after the decimal point will become 10

We'll borrow ten from the thousandths digit after the decimal point and it will change from 10 to 9, and now the ten thousandths digit after the decimal point will become 10

Now that we know how to solve the exercise, let's subtract the ten thousandths after the decimal point:

103=7 10-3=7

Let's subtract the thousandths after the decimal point:

91=8 9-1=8

Let's subtract the hundredths after the decimal point:

92=7 9-2=7

Let's subtract the tenths after the decimal point:

93=6 9-3=6

Finally, let's subtract the whole numbers before the decimal point accordingly:

50=5 5-0=5

71=6 7-1=6

And we get:

76.000010.321365.6787 76.0000\\-10.3213\\65.6787

Answer

65.6787

Exercise #20

Circle the correct answer to the following exercise:

95-31.213

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we'll first add three zeros to the number 95 as follows:

95.00031.213 95.000\\-31.213\\

Now we'll solve the exercise in order:

Let's subtract the thousands after the decimal point:

03= 0-3=

Since we cannot subtract, we'll borrow ten from the tens digit of the whole number before the decimal point, since the other numbers are also zeros.

The tens digit of the whole number before the decimal point will become 4, and the hundreds digit of the whole number before the decimal point will become 10

We'll borrow ten from the hundreds digit before the decimal point and it will change from 10 to 9, and now the tenths digit after the decimal point will become 10

We'll borrow ten from the tenths digit after the decimal point and it will change from 10 to 9, and now the hundredths digit after the decimal point will become 10

We'll borrow ten from the hundredths digit after the decimal point and it will change from 10 to 9, and now the thousandths digit after the decimal point will become 10

Now that we know how to solve the exercise, let's subtract the thousands after the decimal point:

103=7 10-3=7

Let's subtract the hundreds after the decimal point:

91=8 9-1=8

Let's subtract the tenths after the decimal point:

92=7 9-2=7

Finally, let's subtract the whole numbers before the decimal point accordingly.

Remember that we borrowed ten from the tens digit, therefore:

511=3 5-1-1=3

93=6 9-3=6

And we get:

95.00031.21363.787 95.000\\-31.213\\63.787

Answer

63.787